Finite Group Databasebeta

D47×#1796 #26215615

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productD47×#1796

Splittings

FittingC47×#1796 ⋊ C2
SylowC47 ⋊ C2×#1796

Subgroups

subgroupG/H
centerC2#379×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1796C2
socleC2×C47C2×#379
prime radicalC2×2−1+4×D47C2
cosocleC22×C4×C47C24
hypercenter#1796D47
hypocenterC47C2×#1796
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1796

3602 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

725 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168905);